Spin tool is not shown in toolbar when trying to spin a curve
The spin tool does not work with curves, it's specifically made for meshes. There aren't really any alternatives other than rotating around the 3D cursor.

To rotate around the 3D cursor:


Press . to set the pivot point to the 3d cursor.
Position the cursor at the center of the turn.
Extrude e and rotate the curve.


Tweak the handles so it's curved:




If you don't care if the object is a curve you could convert it to a mesh (Altc) and work with it from there.